Open access peer-reviewed Edited Volume


Bruno Carpentieri

Free University of Bozen-Bolzano


Smooth Manifolds Foundational Theorems Differential Forms Integration Topological Spaces Group Theory Calculus on Manifolds Riemannian Geometry Dirac Operators Differential-Algebraic Equations Geometric Integration Algorithms Computer-Graphics

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About the book

A manifold can be defined as a topological space in which the global properties may vary widely and have a complicated structure, but near each point it resembles a Euclidean space. The concept of manifold is central to modern physical mathematics as it provides tools and techniques for the analysis of complex physical systems using simple topological properties of Euclidean spaces. From Riemann's acceptance that a Euclidean space structure was suitable to study the physical knowledge of his time, until the most recent efforts to produce highly accurate higher dimensional manifolds, there has been a tremendous cross-fertilization of theory, ideas and applied numerical algorithms on manifolds based on a vivid interplay between differential geometry, topology, analysis, algebra and physics.

This book intends to provide the reader with a comprehensive overview of the current state-of-the-art in this fascinating and critically important field of mathematics, presenting some of the most important developments of the last years alongside its applications in areas such as computer-graphics, robotics, augmented-reality, machine learning, quantum mechanics and general relativity, to name only a few.

Publishing process

Book initiated and editor appointed

Date completed: June 12th 2020

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: September 1st 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: November 20th 2020

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: January 19th 2021

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About the editor

Bruno Carpentieri

Free University of Bozen-Bolzano

Bruno Carpentieri obtained a Laurea degree in Applied Mathematics in 1997 from Bari University, then he furthered his Ph.D. studies in Computer Science at the National Polytechnic Institute of Toulouse. After some professional experiences as a postdoctoral researcher at the Karl-Franzens University of Graz, as a consultant for an European project in cardiac modelling at CRS4 in Sardinia, as an Assistant Professor at the University of Groningen and finally as a Reader in Applied Mathematics at the Nottingham Trent University, since May 2017 he is holding an Associate Professor appointment in Applied Mathematics at the Faculty of Computer Science, University of Bozen-Bolzano. The specialty of his research is numerical linear algebra with applications and high-performance scientific computing.

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Book chapters authored 2

Books edited 1

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As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact.

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